The discussion below is merely provided for general background information and is not intended to be used as an aid in determining the scope of the claimed subject matter.
Seismic sensor networks are used for seismic imaging in order to provide three-dimensional images allowing detailed examination of the Earth's structure and localization of oil and gas reservoirs. Accurate imaging is crucial for determining the optimal location of drilling and increasing the extraction of the oil or gas out of a reservoir.
Geophones, passive inertial velocity sensors, are the most widely used sensors in the seismic industry due to their good sensitivity (typically better than 10 ng/√Hz between 5 and 30 Hz), low cost and ruggedness. Nevertheless as described in Baeten G. et. al. D. 2013 “The use of low frequencies in a full-waveform inversion and impedance inversion land seismic case study” Geophysical Prospecting 61 701, the higher resolution in deep soil imaging aimed nowadays, requiring low noise vibration sensing at low frequencies (1-5 Hz), is challenging to achieve with standard geophones due to the 40 dB/decade drop of their response below the natural frequency of the proof mass suspension.
In principle, better signal-to-noise ratio could be achievable with lower (<10 Hz) natural frequency geophones, but the poorer achievable manufacturing tolerance in the mechanical parameters, the larger sensitivity of the mechanical response to the deployment angle and the larger distortion figure are considered major disadvantages. Use of arrays of 10 Hz geophones is common in field practice instead. For these reasons, inertial sensors have been developed on the basis of the micro-electromechanical systems (MEMS) technology.
Typically these MEMS sensors include a proof mass that is suspended by springs and the movements of the mass may be detected by a capacitive read-out scheme. Force balance closed-loop configuration may be implemented by integrating electrostatic force actuators in the chip structure. Typically combs of interleaved finger-like structures, both in gap changing and linear configuration, are used for sensing and actuation (see an example in U.S. Pat. No. 5,563,343).
Major advantages of MEMS are considered flat-to-DC amplitude and phase frequency response, very low distortion and independency of the response on the deployment tilt angle. In principle MEMS are also suitable for low cost, high volume production. Self-noise wise, commercial MEMS seismic sensors with resolution better than 25 ng/√Hz above 3 Hz (sensible for oil exploration applications) are nowadays available as e.g. described in the article by Laine J., Mougenot D. 2014 “A high-sensitivity MEMS-based accelerometer” The Leading Edge 33 1234.
Nevertheless even better noise performance at low frequencies would be desirable to improve the quality of seismic imaging. The resolution in MEMS inertial sensors is limited first by the suspension Brownian noise, the level of which is set by the size of the proof mass and by the mechanical dissipation phenomena taking place in the chip. A general expression for the acceleration Brownian noise spectrum abr is given by (Eq. 1)
      a    br    =            1      m        ⁢                  4        ⁢                  K          B                ⁢                  T          ⁡                      (                          D              +                                                k                  ⁢                                                                          ⁢                  ϕ                                                  2                  ⁢                  π                  ⁢                                                                          ⁢                  f                                                      )                              where m is the proof mass, KB is the Boltzmann constant, T is the temperature, D is the viscous damping factor in [kg/s], k is the elastic contribution to the stiffness of the suspension, φ is the internal friction loss angle and f is the frequency. Viscous damping, due to gas drag and squeezed film effects, can be strongly mitigated by packaging the MEMS at low pressure; modern getter based solutions allow stable and reliable vacuum levels down to 1 mTorr. At these pressures the structural damping limit, due to the internal friction (φ≅10−6 for single crystal silicon) of springs and their anchors to the chip substrate, may be reached.
State-of-the-art MEMS seismic sensors achieve Brownian noise levels below 10 ng/√Hz by using proof masses from one to 30 milligrams, depending on the chip design and packaging pressures (see e.g. Milligan D. J. et. al. 2011 “An ultra-low noise MEMS accelerometer for seismic imaging” Proc. IEEE Sensor 2011 1281). The other limit to resolution is set by the readout noise, e.g. by the minimum proof mass displacement detectable by the built-in capacitance sensor. If xn is the equivalent displacement noise spectral density of the capacitance readout, the corresponding acceleration noise spectrum ard is given by (Eq. 2)
      a          r      ⁢                          ⁢      d        =                    x        n            ·      4        ⁢          π      2        ⁢                                        (                                          f                0                2                            -                              f                2                                      )                    2                +                              (                                                            k                  ⁢                                                                          ⁢                  ϕ                                                  2                  ⁢                  π                  ⁢                                                                          ⁢                  m                                            +                              Df                m                                      )                    2                    where f0 is the sensor natural frequency. At f<f0 the Eq.2 simply reduces to an≅(2πf0)2xn. Therefore enhancement of sensitivity at low frequencies can be achieved by reducing either f0 or xn. Lowering the natural frequency requires lowering the stiffness of the suspension springs and/or increasing the mass of the proof mass.
These parameters are however dependent on the MEMS technology and there is little room for varying these parameters without a substantial increase of the complexity of the design and/or fabrication process. In particular it is challenging to create MEMS structures with low stiffness along a desired axis while maintaining high stiffness in the other directions; having spurious modes within the measurement frequency band is not desirable and for this reason state-of-the-art devices are designed with natural frequencies of a few hundreds Hz.
By taking advantage of the electrostatic non-linearity of gap changing sensing/actuation capacitive structures, the stiffness of the mass-spring system can be electrically controlled as described in U.S. Pat. No. 5,852,242. In such a scheme, the dynamics of the mass-spring system is determined by an effective spring constant km+ke, wherein km is the mechanical spring constant and wherein ke is the electrostatic spring constant which has a negative value. In practical embodiments of U.S. Pat. No. 5,852,242 the MEMS inertial sensor structure is processed with a natural frequency of several hundreds of Hz, for the above-mentioned reasons.
Achieving, with the described method, a significant stiffness reduction on such a mechanical system, is only possible by using very narrow gaps in the capacitive structures, combined with large electrostatic forces applied to the sensor proof mass. This limitation can be simply clarified by considering the effect of a parallel plate electrostatic actuator (with gap d and capacitance C) on a mass m suspended by means of a spring with elastic stiffness km (and natural frequency f0): by applying a voltage V between the actuator plates, the electrostatic force on the mass is F=CV2/2d, while the electrostatic negative stiffness is ke=2F/d. By expressing F as a multiple of the suspended mass weight, e.g. F=Nmg, and being km=2πmf02, the electrostatic-to-elastic stiffness ratio is given by (Eq. 3)
            k      e              k      m        =      Ng          2      ⁢              π        2            ⁢              f        0        2            ⁢      d      For example, with f0=1000 Hz this ratio is approximately 0.5N/d(in micron) (Eq.4). Hence, in this case, achieving even only a factor of 2 stiffness reduction, it would require, for instance, to realize capacitive structures with 2 μm gaps and to apply to the proof-mass of the MEMS sensor static forces twice the weight of the proof-mass itself. Creating such structures is possible by means of relatively complex fabrication processes, like the one described in U.S. Pat. No. 6,871,544B1 in which different wafers are stacked on top of each other in order to realize the desired mass-spring and electrode configuration. Further, the need of small gaps implies that the sensor can only be implemented on the basis of a closed-loop configuration. The resolution of such commercially available sensors typically ranges in the order of 30 ng/√Hz.
Instead of reducing the stiffness of the proof mass suspension as in the above-described example, a capacitance readout as described in WO2010/107436 may be used to increase the sensitivity of the MEMS sensor. The readout, combined with a relatively large proof mass (around 30 mg) for limiting the Brownian motion amplitude, allows achieving a sensitivity of the order of 10 ng/√Hz. Such a performance can be obtained by operating the MEMS in open-loop configuration and by using a relatively stiff suspension system, e.g. a natural frequency of a few hundreds of Hz. An alternative means of improving the noise figure of the capacitive readout is described in US2008028857.
Further improvements in the resolution of MEMS inertial sensors may go through implementation of readout systems based on integrated optical interferometry, technology proven in laboratory devices but still requiring complex and expensive fabrication processes that make it, to date, not suitable for applications in large sensor networks.
Hence from the above, it follows that there is a need in the art for improved inertial MEMS sensors that have a sensitivity better than 10 ng/√Hz down to 1 Hz making use of conventional capacitance bridge readout and that are robust and simple to fabricate with high yield in a batch process.